El número de tesis defendidas en el periodo: 4

An artificial neural network (ANN) was applied to study two cored wells with the best data set and the most complete well log data. With their core information and well logs, the selected wells conducted mutual-learning and summarized regularities from that.

In this study, a back-propagation algorithm was applied in the geological artificial neural network system.

Figure 22: Simplified diagram of a back-propagation artificial neural network

In a back-propagation artificial neural network (Bp-ANN), N1 and N2 represent two inputs.

The final output is generated by a linearly weighted sum of all its input. The diagramm is shown as below, where w1 and w2 are the weights of N1 and N2, respectively (Pradhan and Lee, 2010).

N

N

φ

w

w

Output

Input

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The output of the system is usually not the expected value and when the error exists, back- propagation stimulates the system to re-conduct the training to decrease the value of error E (Dedecker et al., 2004). The smaller the error is, the more accurate the output will be (Gardner and Dorling, 1998).

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Figure 24: Demonstration of the artificial neural network where the input is data from two wells and the output is the predicted lithofacies distribution in these two wells

The input in this ANN is the set of wireline logs and core description of Well1 and Well2, where the wireline logs include the curves of GR, RHOB, ILD, ILM, PHIT and PHIE (Qi and Carr, 2006).

Well1 = {Lithofacies1, WirelineLogs1} Well2 = {Lithofacies2, WirelineLogs2}

By applying different numbers of iterations, limiting errors and establishing a probability threshold, one can get the output of predicted lithofacies distribution of both Well1 and Well2.

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Well Correlation by Cores

Carbonate reservoirs are more heterogeneous than are siliciclastic reservoirs, which makes carbonate reservoir characterizations more difficult (Yose et al., 2006). Additionally, wireline logs do not correspond closely to the lithofacies of carbonate rocks. Therefore, cores are normally applied to well correlation. The artificial neural network (ANN) was applied in well-core correlation. Eliasville Caddo Unit #33 and East Eliasville Caddo Unit #46 are the two sample wells, sites of mutual-learning and replicating each lithofacies distribution on well logs. The input of this ANN system is the real core data, represented by L33-A and L46-A in the figure, and six wireline curves, which are gamma-ray (GR), density curves (RHOB), deep induction resistivity logs (ILD), medium induction resistivity logs (ILM), total porosity curves (PHIT), and effective porosity curves (PHIE). The output is the predicted lithofacies of these two wells. Theoretically, if the predicted versions of lithofacies distribution are 100% the same as those of the cores, the algorithm of this artificial neural network is proved to be effective for the model. However, it is normally impossible to duplicate the reality. Practically, if the predicted version of lithofacies resembles to a high extent their real core descriptions (the error E is tolerable and smaller than a given value), the simulation proved to be successful. As a result, when the iteration times of back-propagation cycles are set at 2000 and the error limit is set at 10, the output, denoted by L33-B and L46-B, resembles fairly well their real core data, as is demonstrated in Figure 5-4.

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Figure 25: Well correlation and lithofacies simulation in the Eliasville Caddo Unit #33 well (left) and East Eliasville Caddo Unit #46 well (right).

L33-A and L46-A are both from the cores, which are compared with L33-B and L46B, which are the simulation results. By doing the comparison, several features of this algorithm are clear. First, all the lithofacies appearing in the cores are simulated through ANN. Secondly, the thickness of the intervals in L33-A and L46-A are approximately equivalent to that of L33-B and L46B.

However, there are also some defects in this simulation. The first is that the depth of a certain type of lithofacies might vary in the predicted lithofacies distribution, as exemplified by interval M in L33-A and its corresponding interval in L33-B. In L33-B, phylloid algal wackestone and packstone, indicated in yellow, appears to be lower than expected. Another obvious defect is illustrated by interval N in L46-A and its corresponding interval in L46-B. There are a few beddings of Komia wackestone and mud-dominated packstone within the lithofacies of Komia grainstone and grain-dominated packstone. These beds are thin, having a thickness of less than 1 ft.

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Results are also supposed to run the testing by other cored wells to prove that this methodology is effective for the whole study area.

Figure 26: Lithofacies distribution of the Eliasville Caddo #86 well, from both core description (L86-A) and the artificial neural network’s simulation (L86-B).

In the core from the Eliasville Caddo #86 well, three lithofaices are distinguished: (1) phylloid-algal packstone and wackestone, (2) Komia wackestone and mud-dominated packstone, and (3) bioclast wackestone. Two intervals of Komia wackestone and packstone have thicknesses of 18.3 ft and 7.9 ft with a total of 26.2 ft. The thicknesses of two intervals of phylloid-algal wackestone and packstone are, respectively, 3.4 ft and 1.5 ft, for a total of 4.9 ft. The third type of lithofacies, bioclast wackestone, has a thickness of 12.5 feet. The simulation in L86-B has the best result for bioclast wackestone, which has a thickness of 12.1 ft. The error for this lithofacies in

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terms of thickness is 3.2% and the depth is 0.4 ft moved upward only (demonstrated between two red dashed lines; Figure 4-17). The total thickness simulated for phylloid-algal wackstone and packstone is 4.1 ft, and compared to the 4.9 ft in the core, the error is 16.3%. Instead of only two intervals of this lithofacies, five intervals of this type show up in L86-B. Similarly, Komia wackestone and mud-dominated packstone, has a thickness of 28.6 ft, compared to 26.3 ft in the core. The error percentile is 8.7%.

Figure 27: Lithofacies distribution of the Eliasville Caddo #131 well, from both core description (L131-A) and the artificial neural network’s simulation (L131-B).

The Eliasville Caddo #131 well is another cored well yet it lacks complete core data. In the uppermost part of the well, there is an undefined part with no core data. This part is approximately

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8.7 ft. In L131-B, the corresponding depth is recovered by Komia wackestone and mud-dominated packstone. The thickness of the bioclast wackestone is larger than expected, and the depth is elevated compared to that in L131-A. Phylloid-algal wackestone and packstone is 1.9 ft in L131- A, but, in L131-B, it has been divided into two parts and the in total thickness is 2.1 ft. This error can be tolerated.